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Question: f the mean of a Poisson distribution is 1/2, then the ratio of P (X = 3) to P (X = 2) is -...

f the mean of a Poisson distribution is 1/2, then the ratio of P

(X = 3) to P (X = 2) is -

A

1 : 2

B

1 : 4

C

1 : 6

D

1 : 8

Answer

1 : 6

Explanation

Solution

We have l = E(X) = ½

\ P(X=3)P(X=2)\frac { \mathrm { P } ( \mathrm { X } = 3 ) } { \mathrm { P } ( \mathrm { X } = 2 ) } = e−λ⋅(13!λ3)e−λ⋅(12!λ2)\frac { e ^ { - \lambda } \cdot \left( \frac { 1 } { 3 ! } \lambda ^ { 3 } \right) } { e ^ { - \lambda } \cdot \left( \frac { 1 } { 2 ! } \lambda ^ { 2 } \right) } = λ3\frac { \lambda } { 3 } = 16\frac { 1 } { 6 }